Seeing is believing: Priors, trust, and base rate neglect

Abstract

Kahneman and Tversky (1973) described an effect they called ‘insensitivity to prior probability of outcomes’, later dubbed base rate neglect, which describes people’s tendency to underweight prior information in favor of new data. As probability theory requires that prior probabilities be taken into account, via Bayes’ theorem, the fact that most people fail to do so has been taken as evidence of human irrationality and, by others, of a mismatch between our cognitive processes and the questions being asked (Cosmides & Tooby, 1996). In contrast to both views, we suggest that simplistic Bayesian updating using base rates is not necessarily rational. To that end, we present experiments in which base rate neglect is often the right strategy, and show that people’s base rate usage varies systematically as a function of the extent to which the data that make up a base rate are perceived as trustworthy.

Introduction

In the closing remarks to A Philosophical Essay on Probabilities, Laplace (1814/1951) argues that “the theory of probabilities is at bottom only common sense reduced to calculus; it makes us appreciate with exactitude that which exact minds feel by a sort of instinct without being able ofttimes to give a reason for it”. Within probability theory, Bayes’ rule provides the mechanism by which a set of prior beliefs can be updated in light of evidence, as follows: given a hypothesis, h, which we believe has some prior probability of being correct P(h), if we then observed some data, x, Bayes’ theorem tells us how to find P(h|x), the posterior probability that h is true given that we have now seen x,

$$P(h|x)=\frac{P(x|h)P(h)}{P(x)}\text{.}$$

As to whether Laplace’s claim provides a plausible account of human reasoning, one of the principal sources of discussion is base rate neglect, a phenomenon that seems to contradict the assertion that analytic probabilities are merely formalized versions of people’s intuitions about chance. The general finding is that, when people are provided with prior information (in the form of a base rate) along with new evidence, they typically weight the evidence provided by the new data far more heavily than that provided by the base rates (Kahneman & Tversky, 1973). This tendency to downgrade the value of the prior relative to the likelihood is taken to imply that: firstly, Bayes’ theorem does not provide a complete account of the reasoning employed by people (Villejoubert & Mandel, 2002); and, secondly, that people are therefore suboptimal or biased in their judgments, and may be regarded as acting irrationally. Note, however, that there are two distinct claims here. Clearly, underweighting the base rate information will lead people to make judgments that differ from those provided by a simplistic application of Eq. (1). The charge of irrationality, however, is a stronger claim, and somewhat more questionable.

Traditional approaches to the study of human decision making have tended to assume that rational behavior is best operationalized in terms of the strict adherence to some optimal strategy calculated by the researcher in advance (as is the case in most uses of expected utility theory). Any deviations from this researcher-specified strategy are then deemed to be evidence of irrational behavior. The major problem with this approach is that the manner in which these optimal strategies are designed is often extremely impractical – most notably, no consideration is given to the costs associated with time spent and computations performed. As argued by Todd and Gigerenzer (2000), it is by no means clear that a rational actor should, in fact, expend a great deal of time and effort in computing exact solutions to complicated problems, especially when fast and simple approximations are available.

This accords well with observations such as those made by McKenzie (2003), who argues that rational models should, properly, be regarded as theories but not standards of behavior. This, it is argued, is because apparent errors observed in laboratory tasks actually tend to result from participants’ use of strategies that deliver good results in real world tasks. Thus, while such strategies can be regarded as “irrational” within the context of the specific task, it might in fact be the case that the strategies that are optimal in the experiment would in fact hinder performance in real life.

Guided by these ideas, we consider the question of base rate neglect with respect to how people should appropriately weight base rates and novel information in order to make predictions in real environments. To do so, we present two experiments (in three parts) that manipulate the quality of different sources of data presented to people. In doing so, we depart somewhat from the classic base rate neglect approach; specifically, we design scenarios that minimize the potential computational problems (as explained below) by making explicit what information needs to be aggregated and, instead, manipulate the apparent quality of the data. The results suggest that the strength of base rate neglect effects can be systematically manipulated by altering the trustworthiness of the data – while some people display some base rate neglect, the majority of our participants made decisions in a fashion consistent with assigning different levels of trust to different sources of evidence.